PROCEEDINGS. 
599 
But with the growth of the science mathematicians separate into classes, 
and different nations produce various methods for teaching and cultivat¬ 
ing the science. The English school teaches largely by working examples, 
and lays much stress on the solving of problems. I think there is much 
that is good in this method, since it is well to bring one’s knowledge to 
the test of trial. But when we look over the lists of wranglers at Cam¬ 
bridge and consider the great amount of reading and hard work that is 
done, we feel that for some reason this method does not furnish the best 
results. Apparently it gives too much weight to memory and the training 
for a special trial. The prizes offered in the shape of honors and fellow¬ 
ships are so great that men with money employ experienced coaches and 
tutors, and it is not certain that the ablest mathematicians win. The suc¬ 
cessful coach will not only be a good mathematician, but he must also be 
a man of the world. He will invite the examiners to dinner, gauge them, 
and find out what kind of questions they are likely to set. Having done 
this, he can prepare his students for the contest with a confidence of suc¬ 
cess. Here is a good field for skillful management, and one is not sur¬ 
prised to be told that during the last twenty years more than half the first 
ten wranglers of each year at Cambridge have come from one famous 
coach. These successful men become the examiners of after years, and of 
course this old coach knows the caliber of every one of them. In these 
contests, as described by one of their best men, the main thing is to solve 
a question in twenty minutes, for this is all the time the contestant will 
have at his disposal. To do such work a man must be well drilled in all 
analytical transformations, he must have a great deal of practice in solving 
problems, and, furthermore, he must be quick with his pen and write a 
plain hand. But the real questions of a science cannot be dealt with in 
this manner, and experience teaches us that a man’s ability does not de¬ 
pend on his penmanship ; and although the drill in analysis is valuable 
I. think the habits a man gets from such a course are apt to make him for 
life merely a solver of conundrums and book-questions, or he becomes 
dead scientifically as soon as he is stamped A. B. It has a strange sound 
to be told that to get honors in the great mathematical university of Eng¬ 
land it is a waste of time to read Lagrange, Laplace, and Gauss. But after 
all w T e must acknowledge that this system does produce some able men. 
Turning now to the continent of Europe we see many men in France 
and Germany who spend their lives in the study of pure mathematics. 
These are the men who support the great mathematical journals and who 
are the real pioneers of the science. It is a wonder how they live and find 
time to do so much work. The only answer I can think of is that they 
are content with small salaries and are willing to lead simple lives. These 
men are not problem-solvers as the term is now used. 
In our own country we have only begun scientific work, and in mathe¬ 
matics we have done very little. The tone of our society is opposed to 
such work. Religion and politics, politics and religion, have been and 
still are the subjects which attract the attention of men and furnish the 
